Regarding the AS350: Yes, there are direct mechanical links to the flight controls. In training, disabling the hydraulics has results similar to losing power steering in a car. Some important differences: You lose control assist to all flight controls- pedals, collective, and cyclic. The amount of feedback you'd have to deal with varies with power applied, which is affected by weight and speed.
If I remember the accident scenario correctly, the aircraft ended up on rooftop but upright? If so, the complicating issues for the pilot were the loss of control boost at a high hover (?) and high power setting; some confusion over exactly what was occurring; and humongous attitude and speed variations; all bad when you're in a loss of boost situation. Control displacement takes a fair bit of effort, and that appears to cause a lag in effect. It's also somewhat mentally disorienting in that most of normal flight involves not 'horsing' the controls about and it's physically fatiguing as well.
In training, at least, it doesn't seem to be any big deal. Yet, this scenario ends unhappily far too often for me not to be somewhat concerned.